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Question

asked Oct 19, 2022 109k views

1 Answer

Vlr · Answer 1 · 2022-10-22T17:28:38+0000

Given:

A rectangle with sides 40 and 25.

A circle with radius 8 inside the rectangle.

The area of circle is unshaded.

To find:

The probability that a point (randomly selected) will lie in the unshaded region.

Solution:

The area of the rectangle is:

A_1=Length* Width

A_1=40* 25

A_1=1000

The area of the circle is:

$A_2=\pi r^2$

Where, r is the radius.

$A_2=\pi (8)^2$

$A_2=\pi (64)$

$A_2=64\pi$

$A_2\approx 201.06$

The probability that a point (randomly selected) will lie in the unshaded region is:

$\text{Probability}=\frac{\text{Unshaded region}}{\text{Total region}}$

$\text{Probability}=(A_2)/(A_1)$

$\text{Probability}=(201.06)/(1000)$

$\text{Probability}=0.20106$

Therefore, the required probability is 0.20106.